Get Developments in offshore engineering: wave phenomena and PDF

By John B. Herbich

ISBN-10: 1601191650

ISBN-13: 9781601191656

Drawing from specialists and most sensible researchers from world wide, this ebook offers present advancements in quite a few components that impression offshore and ocean engineering.

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Example text

In the wave-tank simulation, four major numerical tasks are performed by the model: generating waves at the ocean end of the tank, enforcing an appropriate boundary condition at the shore end of the tank, finding the solution of equations of a two-point boundary value problem in space at a given instant in time, and integrating these equations in time. Each task requires special techniques as described in detail by Demirbilek and Webster [5] and because these tasks are crucial, a brief discussion of each task follows.

I i................................... i i ! ~ i )i................................... i i i i ) i~.................................... i i ! i ! i..................................... 02 0 5 10 15 20 25 X Figure 8. 4 sec. These snapshots correspond to waves in tank just before the first wave breaks in Example 2. 080 I 1 ........................................................................................................................................................... : ......................................................................................

Velocity profiles: (62) u = u0 + Ul ; + u2 ;2 w:w0+w,;+w:; 2 (63) Kinematic boundary conditions: w0=0 (64) Wl [~+W2 ~2 = ~ t + u 0 [~x + u l ~ x (65) Continuity equation: U2 -" 0 (66) (restricted theory) UOx + W 1 = 0 (67) Ulx + 2 w 2 = 0 (68) Conservation of momentum: n = 0, x-component: 1 ~2 ~Uot +~" +~ 1 ~2 e Ult +_~1 IB3 U1 W 1 + 1 Ul Ulx +-~1 B2 UO Ulx +'~"lf)2 U1 UOx + [~ U0 UOx 1 ~3 U1 W2 --IBx -3 o Pox P (69) 28 OffshoreEngineering n = 1, x-component: 1 132 Uot +3"1 133 Ult 1~4 +-- 4 Ul W2 + i~4 Ul +'~"1 1~3 Ulx +~"1 Ul Wl = ~ x 3 133 Ul P p UOx + ~ 1 132 UO UOx Plx p (70) n = 2, x-component: 1 [33 U0t 1 ~4 1 +'4 " Ult + ~ [35 Ul 1 Ulx +~- ~4 1 [35 1 ~4 = 1]2 f) +-5 U 1 W 2 + "4" U1 W1 I~x p 1 133 U0 U0x Ul UOx + ' ~ P2x p (71) n = 0, ~-component: 1 ~3 1 ~4 1 ~3 1 ~3 1 i] 2 wit + "3 "2 W2t + "4" u 1 W2x + "3 u 0 W2x + "3 u i w ix + - -1U 0 WIX + 1 ~4 W2 + 2 ~3 2" Wi W + 1 132 Wl2 = - - f ~ + - - - - g ~ 2 ~" P (72) n = 1, ~-component: 1 133 Wit 1 ~4 1 "F'~- W2t +-~ 5 ~5 1 ~4 1 ~4 1 U1 W2x -F-~- U0 W2x +-~U1 Wlx + ~ ~3U 0 W1 + -2- 135 w 2 + 3 ~4 w , w 2 + 1 I ] 3 w ~ = - l ] p + - - -Po -g 5 p 1 ~2 (73) 2 n = 2, ~-component: -41 ~4 Wl t +-1 3 1 ~5 W -I- "5 1 ~6 2t "F g ~6 w E + 3 135 w l w 5 2 1 [35 U0 U l W2x --F 5 + 1 [~4 w 2 = "4 1 ~5 W2x "1-~ 1[~4 U0 W1X U1 W lx -F 4- ~2 -P- + 2 - -P1 --g 1 19 19 3 ~3 (74) In this case, we have a total of eleven equations.

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Developments in offshore engineering: wave phenomena and offshore topics by John B. Herbich


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